Math 270E : Assignment 2

Assigned Wednesday, Oct. 1, 2008, due Wednesday, Oct. 8, 2008

In this assignment you will be experimenting with different methods for solving the two dimensional convection equation.

Download the Assign2 repository from https://www.math.ucla.edu/~anderson/270eSupport/ to your course directory.
Create a separate project for this assignment, or, if using command line versions Linux/Unix, copy the makefile from Assign1 and modify it appropriately to construct a makefile for this assignment. Build the executable.

Files used in this assignment:

ConvectionTest.cpp	Program for testing several different discretizations for solving the convection equation.
ConvectionRoutines.h, ConvectionRoutines.cpp	Convection routine function prototypes and source code
GridParameters.h, RunParameters.h	Parameter class declarations. Declarations for the GridParameters and RunParameters classes.
DoubleArray1D.h, DoubleArray2D.h	A "light" array class that provides dynamic allocation, optional bounds checking and high level array operations. Note: Array indexing starts at 0 ("C" convention)
outputToGNUplot.h, outputToGNUplot.cpp or outputToMatlab.h, outputToMatlab.cpp	Output header file and source for creating GNUplot or Matlab readable data files. Substitute your own output routines if you are not using GNUplot or Matlab.

The main driver program is ConvectionTest.cpp. As the routine is now written, it will prompt you for the input, and, in addition to displaying the errors it will output the solution to a data file at every nth step.

For each of the spatial discretizations, estimate (on the basis of suitable numerical experiments) their rate of convergence when you refine the mesh while keeping the ratio of the timestep to the mesh size constant. Use fourth order Runge-Kutta timestepping when doing your experiments. When doing your experiments, you may want to "comment out " the console output code.
Report the effect of using different order Runge-Kutta schemes for each type of spatial discretization. In particular, when computing a single rotation using a timestep equal to that suggested by the CFL condition, determine which RK scheme gives reasonable results.

What You Should Turn In

Your estimates of the rate of convergence in 1 and the data you used to make these estimates.
Your answers to question 2.